Fault detection for mobile robots using redundant
positioning systems
Paul Sundvall and Patric Jensfelt
Centre for Autonomous Systems, KTH
SE-100 44 Stockholm, Sweden
Abstract— Reliable navigation is a very important part of an
autonomous mobile robot system. This means for instance that
the robot should not lose track of its position, even if unexpected
events like wheel slip and collisions occur. The standard approach
to this problem is to construct a navigation system that is robust
in itself. This paper proposes that detecting faults can also be
made outside the normal navigation system, as an additional fault
detector. Besides increasing the robustness, a means for detecting
deviations is obtained, which can be important for the rest of the
robot system, for instance the top level planner. The method uses
two or more sources of robot position estimates, and compares
them to detect unexpected deviation without getting deceived by
drift or different characteristics in the position systems it gets
information from. Both relative and absolute position sources
can be used, meaning that existing positioning systems already
implemented can be used in the detector. For detection purposes,
an extended Kalman filter is used in conjunction with a CUSUM
test. The detector is able to not only detect faults, but also give
an estimate of when the fault occurred, which is useful for doing
fault recovery. The detector is easy to implement, as it requires no
modification of existing systems. Also the computational demands
are very low. The approach is implemented and demonstrated on
a mobile robot, using odometry and a scan matcher as sources
of position information. It is shown that the system is able to
detect wheel slip in real-time.
I. I NTRODUCTION
For mobile service robots, a crucial part of the system is to
navigate reliably, meaning to move the robot between places
while avoiding losing track of its position. Such functionality
is needed in e.g. fetch-and-carry tasks and supervising tasks.
For such tasks, it is necessary for the robot not to lose track
of its position in order to be successful. Losing position
means that the risk of collision is increased, as there might be
obstacles marked on the robot’s map that are not possible to
detect with normal sensors and thus not captured by obstacle
avoidance mechanisms. An example of such an obstacle is
descending stairs. Clearly, the success of the robot is highly
dependent on the integrity of the navigation system. The
importance of the navigation system for a mobile robot can
be compared to how much an industrial robot is depending
on its joint encoders. If a collision occurs, the robot should
minimize the damage by either doing an emergency stop or
take recovery actions. Such collisions might hurt people or
damage the robot, which should be avoided to the greatest
possible extent.
Faults typically have a low probability of occurring, but
the costs associated with them are high. Most systems work
well under normal operating conditions, but their performance
Fig. 1. A Pioneer robot in collision (see arrow in top right corner) with a
table. This is not observable by the laser scanner (blue), sonars or the bumper
switches since they are vertically displaced compared to the table. At the back
of the robot (left in the picture), there is a caster wheel. As the robot drives
forward against the table, the weight transfers to the caster wheel and the
wheels slip against the floor.
degrade significantly upon unexpected events, such as failing
sensors or undetected obstacles. For applications in a domestic
setting, the environment is changing and there are people moving in the close proximity of the robot. For such applications,
users may not be supervising or may not even be able to help
the robot if an unwanted situation occurs.
There are many things that can make the navigation system
fail, e.g. collisions or sliding against something which makes
the robot rotate, slippage when running over a cable or a
threshold, or because users push the robot. Earlier studies
have shown that users are prone to test the limits of the robot
capabilities, trying to destroy it or harassing it on purpose
[1]. Detecting faults in the navigation system improves the
performance in such situations. An example of a situation
where the navigation will fail is shown in Fig. 1. This situation
could for instance occur if the robot is exploring the world
to build a map of the environment, or if the obstacle is not
included in the existing map. These two examples are valid
for what situations a service robot can encounter. In the case
shown in the figure, there are very few (if any) systems that
can handle the situation, and the robot will almost certainly
lose track of its position. Regardless of how the robot got into
the situation, there is in this case no sensor on the robot that
can detect that the top of the robot is in contact with the table.
As the robot strives forward, the wheels will start spinning on
the floor because of the contact with the table. This situation
could be mitigated by adding more sensors, until the point that
there would be bumpers all over the robot. Adding sensors
increases complexity, space and cost, and does not seem to be
a promising solution.
For the operation of the robot, it might be of equally high
importance to know that there has been a collision as it is
to maintain navigation performance. This implies that robust
navigation is not enough for successful operation, but should
be accompanied with a fault detection system.
II. A PPROACH AND OUTLINE
In the present paper, the approach is to use any two or
more (redundant) localization methods, and compare their
outputs to detect unexpected large deviation. Small deviations
between localization methods are normal due to sensor noise
and algorithm imperfections, while large deviations indicate
that a fault has occurred.
An extended Kalman filter is used to track the outputs from
the localization methods, and the residual of the filter is used
to determine if an unexpectedly large deviation has occurred.
To reduce the risk of false alarms, a CUSUM test is used to
monitor the residual of the Kalman filter.
In the next section, other approaches to the problem are
discussed. The details of the current approach presented in
this paper are provided in Section IV. Experimental results
from an implementation of the approach are shown in Sections V and VI.
III. R ELATED WORK
Increasing robustness has been a driving force for developing navigation methods. In [2], movable doors are detected
and removed from the map in order not to entice the navigation system when doors are opening or closing. Having
people standing around the robot while building a map of the
environment can confuse the robot. In [3], laser echoes from
people are detected and removed prior to feeding the laser data
into the map building system.
A common approach for navigation is to use a Kalman
filter. As the Kalman filter only can approximate a unimodal
probability distribution, methods to handle ambiguous situations have been developed. One example is [4], where multiple
hypothesis are used to represent the uncertainty of the robot
position. Another example is to use particle filters to represent
the uncertainty [5].
Common to the approaches mentioned above is that the
robustness is built into the navigation system, meaning that
changes and tuning needs to be done within those systems. The
present approach is different, as the detection of anomalies is
performed outside the navigation system modules. Implementing detection of faults using an external fault detector might
be easier than changing existing localization modules, unless
you are a domain expert.
The idea of using Kalman filtering for fault detection is not
new. For robot localization, the Kalman filter is very often used
to fuse different sensors. Several contributions for detecting
faulty sensors exist. In [6], a bank of Kalman filters, each
one tuned to a specific fault, is used to do detection. Fault
isolation is obtained by studying which of the residuals are
large. The approach is demonstrated on a robot equipped with
wheel encoders (odometry) and a rate gyro. In this approach,
the detection is implemented in close conjunction with the
sensors. Another approach is presented in [7]. Multiple sensors
are combined to obtain several estimates of robot position,
orientation and speed based on different sensors for each
estimate. The pairwise differences between the estimates are
then used as residuals. Based on what residuals are small
and large, a table mapping high residuals to specific faults
is used to isolate faults. Navigation is then performed with
the subset of sensors that are considered functioning. It is not
clear how the algorithm handles accelerometer and gyroscope
drift, which would cause the position estimates to drift away
compared to the odometry based estimates. An important
difference between the proposed method and the methods in
[6] and [7] is that those methods operate on a sensor level,
while the proposed method operates on a higher level.
A way to increase the possibility to detect and accommodate
faults is to add more sensors. Hardware may be doubled or
more (Hardware redundancy), or redundancy can be added by
observing the same thing with different sensors. One approach
based on the latter is “gyrodometry”, presented in [8]. In
this case, the difference of yaw rate reported by a gyro and
odometry is thresholded to decide which source of rotational
speed should be used for positioning.
In [9], a particle filter is used for fault detection and
isolation. Several discrete states are used, one for each fault
mode, and an associated model for the continuous states is
used for every mode. Particle filters are very powerful for
tracking systems, and output a probability distribution over
the states, given as samples (particles). It can be used for
nonlinear, non-Gaussian and multi modal distributions and
outperforms the Kalman filter in such cases. The drawback
is that the computational demands increase fast with the state
dimension, even if there are means for increased efficiency
[9]. Another drawback is that a fault model is needed to track
the probability of being in a fault state. With a Kalman filter
tracking the normal state, it is possible to test for deviation
from the normal (fault free) model, thus requiring a model
only for normal behaviour.
IV. M ODELLING
As previously mentioned, the approach is to use existing
systems or sensors (“pose providers”) for obtaining updates on
robot position or movement. All these systems have their own
for each pose provider. Having a pose provider that slowly
drifts, as for instance odometry, does however lead to cross
couplings between noise sources and robot speed and is thus
more difficult to track.
A standard first order dynamic model is used for the
evolvement of the output from the pose providers:
xt+1
yt
Fig. 2.
The pose providers might use different coordinate systems, as
indicated by the figure. Drift in the pose providers will make the coordinate
systems move around with time.
characteristics of drift and noise. In the following sections, a
model is presented that makes it possible to decide what is a
normal deviation and what is not.
A. Pose providers
The term pose provider is used for sensors or systems that
deliver estimates of the robot’s position. The estimates do
not need to be in the same coordinate system or have the
same update rate. See Fig. 2 for a visualization of different
pose providers having different meanings of where the robot
is. Examples of pose providers are odometry, which can be
regarded as a sensor, and SLAM which is an algorithm.
Other examples are scan matching based odometry [10], visual
odometry [11] and wireless localization [12]. It is important
that the pose providers provide redundancy. Many navigation
modules assume that the odometry is quite reliable and will
fall back to odometry when the sensor readings do not match.
In that case, odometry and the navigation module will behave
equal. Since there is no redundancy left, there is no way to
see that a fault has occurred.
As mobile robots often are equipped with many different
types of sensors, and there are several algorithms that use
a subset of the sensors, it is not difficult finding independent pose providers. An example of a basic system is to
use odometry as one pose provider and an integrator that
integrates motion control commands to position as a second
pose provider.
An important property of a pose provider is if the estimation
error is bounded or not. Inertial navigation systems and odometry have position errors that grow over time, while systems
like SLAM and map based navigation systems typically have
position errors that remain bounded. The approach presented
here can handle both types of systems.
B. System model
To detect deviation between the pose providers, a model is
used
to predict the readings. A set of three state variables ri =
T
x y θ is used for every pose provider i, which corresponds
to rectilinear position and orientation of the robot, in the frame
of each pose provider.
The particular choice of the state vector leads to a nearly
linear system. Another possibility is to choose the state to
be the true position augmented with a coordinate transform
= xt + Gt (xt )wt
= xt + vt
cov(wt ) = Qt (xt )
(1)
cov(vt ) = Rt
T
where x is the aggregated state vector r1T r2T . . . rpT
for p pose providers. The process noise w corresponds to
commanded motion as well as noise inherent within the
pose providers. The model assumes that the control signal
(speed reference uc ) of the robot is an unknown stochastic
variable, and included in the process noise vector w. One
can argue that the commanded motion of the robot is known
and should be included as a deterministic input signal in
(1). However, experiments have shown that this does not
contribute significantly to detection performance. The increase
in performance does not weigh up the added complexity of
implementing the deterministic signal. On some systems, it
might not even be possible to get this signal, for instance
when the robot is controlled by the hardware directly or by
another piece of software. If the control signal is available
(speed reference), it can be externally integrated into pose
using an appropriate dynamic model and then used as a pose
provider in the present framework. The dynamic model for the
relation between control signal and pose could be arbitrarily
complex without affecting the structure of the fault detector, as
only the output of the algorithm is read into the fault detector.
The measurements are the readings of the pose providers,
and the influence of sensor noise is captured in the process
noise w, and not the measurement noise v. This is further
discussed in the remainder of the section.
C. Model input and process noise
The process noise w is a 2 + (2 + 3)p vector which is used
to model both the commanded motion of the robot as well
as disturbances and imperfection within each pose provider.
The latter will give rise to drift in the pose providers. In the
following equations, the matrices are given for p = 2 pose
providers. Extending to use more pose providers is straight
forward.
 c
 c

u
Q
ue,1 


Qe,1
 e,2 


e,2



 (2)
Q
w = u  Q = 

c,1
c,1
u 


Q
uc,2
Qc,2


1
∆T cos(θi )
0
G G1 0 I3 0
0 
Gt =
Gi =  ∆T sin(θi )
G2 0 G2 0 I3
0
∆T
(3)
Each part of the process noise vector represents different
sources for driving the pose providers. The noise is assumed
to be zero mean and white.
Common robot speed: The first and dominating part
of
the
process
noise vector is uc , the common robot speed
T
ux uω . As the robot moves, uc is the part of the model
that captures this. In absence of model errors, pose provider
errors and noise, it would be the only nonzero part of the
process noise. As previously mentioned, the commanded motion is considered to be an unknown stochastic variable. If the
speed reference is known, or there is a model for how the robot
speed evolves, there might be room for improvement on this
part of the model. See the previous section for a discussion.
There is however an advantage in considering the robot speed
to be an unknown disturbance, as there is no need to implement
a coupling from the reference speed signal (fed to the robot
hardware) to the fault detector.
Pose provider robot frame drift: A part of the drift ue,i
of the pose provider
is modeled
as additive input of the robot
T
speed ue,i = v e,i ω e,i . Having a system that integrates
signals from robot fixed speed sensors will be subject to this
type of drift.
Pose provider Cartesian frame drift: As ue,i models drift
relative to the robot frame, uc,i
models drift in a Cartesian
c,i T
c,i
c,i
c,i
frame. u = vx
represents noise that models
vy
vθ
a drift in all states simultaneously, and has the effect of
alleviating problems arising from linearization and model
errors. An important assumption that is made, is that the noise
is uncorrelated. The process noise gain matrix G is composed
of blocks Gi which are linearized around the current heading
angle θi of the corresponding pose provider. ∆T is the time
elapsed since the last update.
The characteristics of the system changes with speed. For
instance odometry has a larger drift the higher speed the
robot operates at1 . Other types of pose providers, like wireless
localization, or inertial navigation, might have drift nearly
independent of speed. To accommodate for these effects of
changing speed, some elements of the noise intensity matrix
Q are scaled with a factor k defined in (4). A similar scaling
can be found in [13]. In this paper, a small offset α is added
to the scaling factor k, to avoid unreasonable low noise at
standstill. The offset also alleviates problems of having a
slight delay in calculating the factor. Normalization constants
v̄i , i = x, y, θ (see 4) are set to normal driving speed of
the robot, and make k approximately 1 at normal speed, and
α 1 at standstill. The reason for scaling the covariance is
that adding independent uncertainty Q/n in n steps obtains Q
total increase of uncertainty, independent of n.
s 2 2
2
vx
vy
vθ
k=
+
+
+α
(4)
v̄x
v̄y
v̄θ
D. Measurement noise
As the imperfection of the pose providers is captured in
the drift model, there is no regular measurement noise v, as
all effects from sensor noise and algorithm shortcomings in
the pose providers are represented in the process noise w.
1 This
reflects that the uncertainty per traversed distance is constant
There will however be effects from scheduling jitter, which is
especially important when implementing the fault detector in
a non real-time system. Also, communication delays between
sensors and receiving system might cause jitter. Effects from
finite machine precision and interpolation errors might also
be captured by the measurement noise. The measurement
noise covariance matrix has been selected diagonal, where the
elements have been chosen as a fraction of the typical motion
between two time steps and the fraction corresponds to the
size of the jitter compared to the sampling time. Having a
nonzero R is also beneficial for the numerical properties of
tracking the state, as R = 0 indicates that the measurements
are exact, and can cause inconsistencies in the estimate.
E. Tracking the state
The pose providers are monitored using an extended Kalman
filter (EKF). In this way, an estimate x̂ and an associated
covariance matrix P is calculated every time step. The purpose
of tracking is not to get the estimate of the output, but instead
to tell whether the pose providers agree or not. In the ideal
case, the innovation (predicted output error) e = y − C x̂
from the Kalman filter is Gaussian and white, given that
the model assumptions hold and that linearization effects
are negligible. When something abrupt happens like sensor
malfunction, wheel slip or collision, the model will not be
valid, and the innovation e will not be Gaussian and white.
Thus, the innovation can be used to monitor the system.
At startup, the filter must be initialized. By setting the initial
covariance P0|−1 to a high value βI, β 1, the filter will
rapidly converge to the correct values. Having one or more
pose providers start at a large nonzero position is thus not a
problem. If the pose providers deliver data at different rates or
readings are missing, the Kalman filter provides means to handle such situations. The Kalman filter theory is well developed,
and provides several tools. See for instance [14]. An alternative
to use EKF might be to compare the speeds from the pose
providers directly, as done in [7]. This is however not straight
forward, as different noise characteristics make it difficult
to reason if changes are large or not. Comparing absolute
sensors (GPS-like) and relative sensors like accelerometers is
not easy. The naive approach of comparing, by differentiating
the absolute position and comparing it to the integral of the
accelerometer signal would suffer from noise amplification and
drift.
F. Detecting abrupt changes
From the Kalman filter, the innovation e is obtained. The
associated covariance will be Re = P + R. A test statistic
is obtained by the Mahalanobis distance st = eT Re−1 e which
will be χ2 distributed with 3p degrees of freedom. All of the
above is true when the model assumptions hold. A simple test
of when to alarm for faults is to set a threshold on st . This
can be done using a standard table, or from monitored levels
of the test statistic.
However, this is sensitive to outliers in st , which can cause
false alarms. To avoid this, st is fed into a detector that takes
in this paper, see [16], which also includes some guidelines
for how to select them.
V. I MPLEMENTATION
To test the proposed method, it has been implemented on a
PowerBot robot from ActivMedia. The robot is equipped with
odometry and a SICK laser scanner among other sensors. The
odometry system can directly be used as a pose provider. As
a second provider, a scan matching routine was implemented
which provides a source of position information independent
of odometry.
A. Scan matching
Fig. 3. Detail of an alarm from the CUSUM test: The blue curve is the test
variable gt . The alarms are marked with circles at the times they are raised,
and the reported time talarm of the first alarm is marked with a vertical line.
the size and duration of the test statistic into account.
G. CUSUM test
The CUSUM test (see for instance [15]) is a test for
detecting positive changes in a positive (noisy) scalar signal. In
short, the test will alarm for a single sample being extremely
large, or several consecutive samples being unexpectedly large.
The algorithm is as follows:
gt = gt−1 + st − v
if (gt < 0) then talarm = t, gt = 0
if (gt > h) then raise alarm and set gt = 0
The test will thus be less sensitive to outliers than simply
thresholding on the test statistic directly. There are two parameters in the test, the drift value v > 0 and the alarm
threshold h > v. A simplified description is that v is related
to what level the input to the detector normally has, and h is
adjusted to trade off false alarms and risk of missed detection.
Since the Kalman filter after a disturbance will slowly adapt
to the new data, faults will only give residuals under a limited
time. Therefore, the detector must not be too slow. It is also
important that the alarm is not delayed more than necessary
after an unexpected event, in order not to worsen the situation.
The CUSUM test can estimate when the change in the signal
has occurred [15]. This is given by the last reset time talarm .
An example of an alarm time obtained with this method is
shown in Fig. 3. Upon alarm, this information can be used
to perform recovery actions on the navigation system. For
instance, estimation of the current position can be carried
out on stored sensor data from the time of when the fault
was believed to occur and forward, where faulty sensors are
excluded from the analysis. The memory of old sensor data
can be of finite length, as a fault alarm probably will come
rather quickly or not at all.
H. Setting filter parameters
The approach has shown to be quite insensitive to the
parameters. For the parameter values used in the experiments
A memoryless scan matching algorithm is implemented,
inspired by [17]. As laser scans come in, they are matched
to the previous scan and the relative motion is extracted. The
pose of the robot is integrated using the relative motion. Using
it this way, one can regard the scan matcher as laser based
odometry. Since the match of two consecutive scans will have
an error that is mainly independent of the robot motion, the
error model with Cartesian noise dominates the drift. The size
of the scan matcher error is for the speed range considered
here nearly independent of the speed, and the corresponding
parts of Q can thus be held constant.
VI. E XPERIMENTAL RESULTS
A. Experiment setup
During the experiments, the robot moved around autonomously using the Nearness Diagram algorithm [18]. The
experimental environment is a room furnished with sofas,
tables and bookshelves to resemble a domestic living room
in size and materials. As the robot is moving around in the
room, it has been pushed to induce wheel slip. The algorithm
was run in realtime on a standard laptop computer, connected
via wireless network to the robot and its sensors.
B. Results
The filter has been tested during several sessions, with both
fault free and faulty data. No false alarms were triggered
during the fault free sessions, even if the robot was forced
to do fast moves with the obstacle avoidance behaviour.
This was triggered by suddenly walking into the field of
view of the laser scanner, close to the robot. Faults were
injected by pushing the robot manually, while it was moving
autonomously between waypoints. An example of output from
such an experiment with faulty data is shown here. The
Mahalanobis distance st from the Kalman filter is shown in
Fig. 4. One can clearly see when the robot has been pushed
(multiple times). One can also see that the residual is very
low during the beginning of the test, when no fault is present.
The corresponding test variable gt and its threshold is shown
in Fig. 5. Each time it exceeds the threshold, gt is reset to
zero and an alarm is raised. The alarm times are marked with
circles in the figure. Several alarms are raised after each other.
A detail of the first alarm is shown in Fig. 3.
skidding on the floor), the proposed fault detector would have
detected the abnormal situation.
VIII. F UTURE WORK
The crucial part for detection using the proposed framework
is that the fault model is accurate. In some situations, pose
providers can adjust their position estimate abruptly, which
might not be captured by the drift model. Such cases may be
handled better, if the pose provider can give information of its
uncertainty.
R EFERENCES
Fig. 4. Weighted residual st from the Kalman filter from test with robot
being pushed several times. The pushes are clearly visible as peaks in st . The
first 25 seconds are fault free and the residual is small.
Fig. 5. Output from CUSUM test with robot being pushed several times.
When the test variable gt exceeds the threshold, an alarm is generated (marked
with circles) and it is reset. The weighted residual from Fig. 4 is used as input
for the detector.
VII. S UMMARY AND CONCLUSIONS
The proposed system is shown to be able to detect wheel slip
in realtime. The system handles initially unknown coordinate
system and different noise characteristics. The approach is
demonstrated using two pose providers, odometry and scan
matching. It is shown that it is possible to detect faults at a
higher level than processing the sensor data directly. Existing
navigation modules can be used, and the parameters that are
needed for the module are quite easy to obtain. By reusing
existing navigation modules, domain knowledge built into
these systems can be utilized. This way, modularity of the
system is kept.
No specific fault model is needed, which is beneficial
regarding the effort needed for implementation, but does not
take advantage of information about faults that may be known.
The algorithm does not isolate faults (indicate the source
of fault), which maybe can be achieved by combining pose
providers pairwise.
Returning to the situation shown in Fig. 1 (the robot
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